Title: Effect of disaster and balking on M/M/1 driven fluid queue with working vacation

Authors: Madhu Jain; Anshul Kumar

Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Haridwar, Uttarakhand-247 667, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Haridwar, Uttarakhand-247 667, India

Abstract: The fluid models are suitable for modelling traffic when individual arrival units have little effect on the system's performance. This paper aims to study the fluid model for the queueing scenario driven by the features of vacationing server, disaster, and balking. By introducing vacation strategy to the fluid model, we can provide greater flexibility for the design and control of input and output rates. By introducing the multiple working vacation strategy to the fluid model, we can provide greater flexibility to design and control the server's vacationing time and output. Continuing fraction and generating function methodologies are used to solve the fundamental framework of differential-difference equations that regulates the operation. The steady state probabilities for the different states of the fluid model have been found explicitly. The stationary distribution of the buffer content has also been derived in terms of the modified Bessel function of the first kind.

Keywords: fluid queue; working vacation; disaster; balking; generating function; continued fraction.

DOI: 10.1504/IJMOR.2022.127380

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.3, pp.359 - 371

Received: 01 Jan 2021
Accepted: 23 Aug 2021
Published online: 01 Dec 2022 *

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